(Blender Game Engine) Walk and Run cycle sound problems
Analyse

Your setup is not exclusive.

This means you can (and do) activate both actuators at the same time. This happens as both are listening to the same keyboard key W. The only difference is the key modifier Left Shift.

Logical Condition - method

You need to exclude the key of the opposite operation when triggering the first operation. 

You can do that with an additional keyboard sensor listening to Left Shift as well, but inverting the output [Invert].

This way the logic will be:

W + not Left Shift -> first actuator
W + Left Shift -> second actuator

Due to the exclusive conditions the actuators will run exclusive too.

State - method

A better implementation is to use the build-in state machine. This way the operations are guarantied exclusive. You can even use the same key to toggle between walking and running.
Example:

State 1: waiting

State 2: walking

State 3: running


waiting: when W -> walking
walking: when not W -> waiting
waiting: when Shift -> running
walking: when not W -> waiting
waiting: when not Shift -> walking